Question

From a sample with nequals8​, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using​ Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions.

Answer 1

Answer:

75% of the households have between 2 and 6 televisions

Step-by-step explanation:

From the question, we can deduce the following;

sample size n= 8

sample mean μ = 4

standard deviation σ = 1

Using Chebychev’s theorem;

P(2 ≤ X ≤ 6) = P(2-4 ≤ (X - μ) ≤ 6-4)

= P(-2 ≤ (X-μ) ≤ 2) = P(|X-μ| ≤ kσ) ≥ (1 - 1/k^2) ≥ (1- 1/2^) = 1- 0.25 = 0.75 ( same as 75%)